Related papers: The Logarithmic Super Divergence and Statistical I…
This paper introduces a new superfamily of divergences that is similar in spirit to the S-divergence family introduced by Ghosh et al. (2013). This new family serves as an umbrella that contains the logarithmic power divergence family…
Minimum divergence procedures based on the density power divergence and the logarithmic density power divergence have been extremely popular and successful in generating inference procedures which combine a high degree of model efficiency…
Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to classical techniques based on maximum likelihood and related methods. Basu et al. (1998) introduced the density power divergence…
M-estimators offer simple robust alternatives to the maximum likelihood estimator. Much of the robustness literature, however, has focused on the problems of location, location-scale and regression estimation rather than on estimation of…
Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical techniques based on maximum likelihood and related methods. Recently Ghosh et al. (2013) proposed a general class…
Divergence measures have a long association with statistical inference, machine learning and information theory. The density power divergence and related measures have produced many useful (and popular) statistical procedures, which provide…
Preserving the robustness of the procedure has, at the present time, become almost a default requirement for statistical data analysis. Since efficiency at the model and robustness under misspecification of the model are often in conflict,…
Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical maximum likelihood based techniques. Recently Ghosh et al. (2013) proposed a general class of divergence measures…
Minimum divergence estimators provide a natural choice of estimators in a statistical inference problem. Different properties of various families of these divergence measures such as Hellinger distance, power divergence, density power…
Density-based minimum divergence procedures represent popular techniques in parametric statistical inference. They combine strong robustness properties with high (sometimes full) asymptotic efficiency. Among density-based minimum distance…
In any parametric inference problem, the robustness of the procedure is a real concern. A procedure which retains a high degree of efficiency under the model and simultaneously provides stable inference under data contamination is…
The aim of this note is to announce some results about the probabilistic and deterministic asymptotic properties of linear groups. The first one is the analogue, for norms of random matrix products, of the classical theorem of Cramer on…
In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed. The popular density power divergence (DPD) class of estimators is a sub-class of Bregman divergences. We propose and study a new…
The most popular hypothesis testing procedure, the likelihood ratio test, is known to be highly non-robust in many real situations. Basu et al. (2013a) provided an alternative robust procedure of hypothesis testing based on the density…
Privacy preservation in machine learning, particularly through Differentially Private Stochastic Gradient Descent (DP-SGD), is critical for sensitive data analysis. However, existing statistical inference methods for SGD predominantly focus…
We prove the large deviation principle (LDP) for posterior distributions arising from subfamilies of full exponential families, allowing misspecification of the model. Moreover, motivated by the so-called inverse Sanov Theorem (see e.g.…
The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing works focus on the convergence of the objective function…
This paper deals with four types of point estimators based on minimization of information-theoretic divergences between hypothetical and empirical distributions. These were introduced (i) by Liese & Vajda (2006) and independently…
We study a new kind of proximity graphs called proportional-edge proximity catch digraphs (PCDs)in a randomized setting. PCDs are a special kind of random catch digraphs that have been developed recently and have applications in statistical…
In this study, we discuss the relationship between two families of density-power-based divergences with functional degrees of freedom -- the H\"{o}lder divergence and the functional density power divergence (FDPD) -- based on their…